The updates in (REF ) could be represented as a linear mapping system. Following [1]}, \( {^{k+1}=\rho _p\bar{}^{k+1}+\bar{}^{k}} \)  is sufficient to represent the system dynamics, where \(\bar{}^{k+1}=[^{k+1}_1;\dots ;^{k+1}_i;\dots ;^{k+1}_b]\in \operatorname{{R}}^{bp\times 1}\) , and \(\bar{}^{k}=[^{k}_1;\dots ;^{k}_i;\dots ;^{k}_b]\in \operatorname{{R}}^{bp\times 1}\) . The mapping matrix of the primal distributed ADMM is given by
\( {_{p}=\left(--\left(+\frac{}{\rho _p}\right)^{-1}\right)(-2)} \) 
